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On solubility and supersolubility of some classes of finite groups

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Science China Mathematics 2009年第2期52卷 272-286页

作者： shum kar ping SKIBA Alexander N. Department of Mathematics University of Hong Kong Department of Mathematics Francisk Skorina Gomel State University

AbstractLet G be a finite group and H a subgroup of G. Then H is said to be S-permutable in G if HP = PH for all Sylow subgroups P of G. Let H sG be the subgroup of H generated by all those subgroups of H which are S-permutable in G. Then we say that H is S-embedded in G if G has a normal subgroup T and an S-permutable subgroup C such that T ∩ H ? H sG and HT = C.Our main result is the followingTheorem AA group G is supersoluble if and only if for every non-cyclic Sylow subgroup P of the generalized Fitting subgroup F*(G) of G, at least one of the following holds: Every maximal subgroup of P is S-embedded in G.Every cyclic subgroup H of P with prime order or order 4 (if P is a non-abelian 2-group and H ? Z ∞ (G)) is S-embedded in G.

关键词： S-permutable subgroups S-embedded subgroups saturated formations generalized Fitting subgroups supersoluble groups 20D10 20D20 20D25

Congruences on ideal nil-extension of completely regular semigroups

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Chinese Science Bulletin 1998年第5期43卷 379-381页

作者： REN Xueming 1, 2 GUO Yuqi 2 and CEN Jiaping (shum kar-ping) 31. Department of Mathematics, Xi’an University of Architecture & Technology, Xi’an 710055, China 2. Department of Mathematics, Yunnan University, Kunming 650091, China 3. Department of Department of Mathematics Xi’an University of Architecture & Technology Xi’an China Department of Mathematics Yunnan University Kunming China Department of Mathematics Chinese University of Hong Kong Hong Kong

Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?

关键词： completely regular semigroups ideal nil-extension congruences.

The construction of orthodox super rpp semigroups

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Science China Mathematics 2004年第4期47卷 552-565页

作者： He Yong Guo Yuqi kar ping shum School of Computer Science Hunan University of Science&TechnologyXiangtan 411201China Department of Mathematics Southwest Normal UniversityChongqing 400715China Department of Mathematics Soochow UniversitySuzhou 215000China Faculty of Science The Chinese University of Hong KongShatinN.T.Hong KongChina

We define orthodox super rpp semigroups and study their semilattice decompositions. Standard representation theorem of orthodox super rpp semigroups whose subband of idempotents is in the varieties of bands described ... 详细信息

关键词： orthodox super rpp semigroup, band-like extension, left cancellative plank, semilattice decomposition, standard representation.

A Survey on Single-Valued Neutrosophic K-Algebras

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Journal of Mathematical Research with Applications 2020年第3期40卷 221-245页

作者： Muhammad AKRAM kar-ping shum Department of Mathematics University of the PunjabNew Campus Institute of Mathematics Yunnan University

In this survey, we first present a brief overview of logical algebras. We then discuss concepts of single-valued neutrosophic K-subalgebras, single-valued neutrosophic soft K-algebras and single-valued neutrosophic topological K-algebras. Moreover, we discuss various fundamental concepts which include interior, closure, C5-connectivity, super connectivity, compactness and Hausdorffness of single-valued neutrosophic topological K-algebras.

关键词： K-algebras single-valued neutrosophic sets homomorphism neutrosophic topological K-algebras

P-Condense and LP-Condensing Operatorson Semilattices,Join-Complete Lattices and Some Inverse Semigroups

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Communications in Mathematics and Statistics 2016年第4期4卷 435-447页

作者： Yong He Wei Tian kar ping shum School of Computer Science and Engineering Hunan University of Science and TechnologyXiangtan 411201HunanChina Intelligent Research Institute SANY Heavy Industry CO.LtdChangsha 410100HunanChina3 Institute of Mathematics Yunnan UniversityKunming 650091YunnanChina

In this paper,the concepts of-condensing operator and 69-condensingoperator on a semigroup are *** we describe the-condensing operatorsand the 69-condensing operators on semilattices,join-complete lattices,and *** an application of our results,we also show that the unary operations*:Hg→Hg-1 Hg and*:Hg→HG on the coset semigroupK(G)of a group G are-condensing ***,a necessary and sufficient condition for theseoperators to be 69-condensing operators is *** further results on condensesemigroups considered by Chen et al.(Acta ***.119:281-305,2008)arediscussed and obtained in this paper.

关键词： P-condensing operator LP-condensing operator Upper closureoperator Join-complete congruence Join-complete lattice congruence Coset semigroup of a group

Single-Valued Neutrosophic Lie Algebras

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Journal of Mathematical Research with Applications 2019年第2期39卷 141-152页

作者： Muhammad AKRAM Hina GULZAR kar ping shum Department of Mathematics University of the Punjab New Campus Institute of Mathematics Yunnan University

A single-valued neutrosophic(SVN) set is a powerful general formal framework that generalizes the concept of fuzzy set and intuitionistic fuzzy set. In SVN set, indeterminacy is quantified explicitly, and truth membership, indeterminacy membership, and falsity membership are independent. In this paper, we apply the notion of SVN sets to Lie algebras. We develop the concepts of SVN Lie subalgebras and SVN Lie ideals. We describe some interesting results of SVN Lie ideals.

关键词： Single-valued neutrosophic sets Lie ideals Lie algebras

A review of geometry-confined perovskite morphologies:From synthesis to efficient optoelectronic applications

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Nano Research 2022年第8期15卷 7402-7431页

作者： Jinshuai Zhang Perry ping shum Lei Su School of Engineering and Materials Science Queen Mary University of LondonLondon E14NSUK College of Engineering Department of Electrical and Electronic EngineeringSouthern University of Science and TechnologyShenzhen 518055China

With the continuous study of metal halide perovskite,geometry-confined technologies have been widely applied to reduce the material dimensionality and to produce pre-designed structures,which can tune optical reflectance,scattering,and absorption,thereby optimizing the performance of perovskite-based optoelectronic devices and improving their commercial *** morphologies of perovskite active layer play a pivotal role in optoelectronic properties and the resulting device *** this review,we systematically summarized recent progress in the preparation and manufacture of various perovskite geometry-confined morphologies,as well as their promising advances in different optoelectronic applications,including photodetectors,solar cells(SCs),lasers,and light-emitting diodes(LEDs).In addition,the remaining challenges and further improvements of preparation unique geometry-confined perovskite morphologies for next-generation high quality optoelectronic devices are discussed.

关键词： geometry confinement metal halide perovskite controllable morphology optoelectronics

On 2-Absorbing Quasi-Primary Ideals in Commutative Rings

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Communications in Mathematics and Statistics 2016年第1期4卷 55-62页

作者： Unsal Tekir Suat Koç Kursat Hakan Oral kar ping shum Department of Mathematics Marmara UniversityIstanbulTurkey Department of Mathematics Yildiz Technical UniversityIstanbulTurkey Institute of Mathematics Yunnan UniversityKunming 650091People's Republic of China

Let R be a commutative ring with nonzero *** this article,weintroduce the notion of 2-absorbing quasi-primary ideal which is a generalization ofquasi-primary *** define a proper ideal I of R to be 2-absorbing quasi primaryif√1 is a 2-absorbing ideal of R.A number of results concerning 2-absorbing quasi-primary ideals and examples of 2-absorbing quasi-primary ideals are given.

关键词： Prime ideal 2-Absorbing ideal 2-Absorbing quasi-primary ideal

Interval Valued (∈,∈ ∨q)-Fuzzy Filters of MTL-Algebras

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Journal of Mathematical Research and Exposition 2010年第2期30卷 265-276页

作者： Xue Ling MA Jian Ming ZHAN kar ping shum Department of Mathematics Hubei Institute for Nationalities Hubei 445000 P. R. China Department of Mathematics The University of Hong Kong Hong Kong P. R. China (SAR)

The concepts of interval valued （∈,∈ ∨q）-fuzzy Boolean, MV - and G- filters in a MTL-algebra are introduced. The properties of these generalized fuzzy filters are studied and in particular, the relationships betw... 详细信息

关键词： MTL-algebra filter interval valued (∈,∈ ∨q)-fuzzy (Boolean, MV- and G-) filters.